A search is presented for massive long-lived particles decaying into a muon
and two quarks. The dataset consists of proton-proton interactions at
centre-of-mass energies of 7 and 8 TeV, corresponding to integrated
luminosities of 1 and 2 1/fb, respectively. The analysis is performed assuming
a set of production mechanisms with simple topologies, including the production
of a Higgs-like particle decaying into two long-lived particles. The mass range
from 20 to 80 GeV and lifetimes from 5 to 100 ps are explored. Results are also
interpreted in terms of neutralino production in different supersymmetric
models, with masses in the 23-198 GeV range. No excess above the background
expectation is observed and upper limits are set on the production
cross-section for various points in the parameter space of theoretical models.

The ratio of branching fractions ${\cal{R}}(D^{*-})\equiv {\cal{B}}(B^0 \to
D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$ is measured
using a data sample of proton-proton collisions collected with the LHCb
detector at center-of-mass energies of 7 and 8 TeV, corresponding to an
integrated luminosity of 3$~$fb$^{-1}$. The $\tau$ lepton is reconstructed with
three charged pions in the final state. A novel method is used that exploits
the different vertex topologies of signal and backgrounds to isolate samples of
semitauonic decays of $b$ hadrons with high purity. Using the $B^0 \to
D^{*-}\pi^+\pi^-\pi^+$ decay as the normalization channel, the ratio
${\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to
D^{*-}\pi^+\pi^-\pi^+)$ is measured to be $1.97 \pm 0.13 \pm 0.18$, where the
first uncertainty is statistical and the second systematic. An average of
branching fraction measurements for the normalization channel is used to derive
${\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau}) = (1.42 \pm 0.094 \pm 0.129 \pm
0.054) \%$, where the third uncertainty is due to the limited knowledge of
${\cal{B}}(B^0\to D^{*-}\pi^+\pi^-\pi^+)$. A test of lepton flavor universality
is performed using the well-measured branching fraction ${\cal{B}}(B^0 \to
D^{*-} \mu^+\nu_{\mu})$ to compute ${\cal{R}}(D^{*-}) = 0.291 \pm 0.019 \pm
0.026 \pm 0.013$, where the third uncertainty originates from the uncertainties
on ${\cal{B}}(B^0 \to D^{*-}\pi^+\pi^-\pi^+)$ and ${\cal{B}}(B^0 \to D^{*-}
\mu^+\nu_{\mu})$. This measurement is in agreement with the Standard Model
prediction and with previous measurements.

The ratio of branching fractions ${\cal{R}}(D^{*-})\equiv {\cal{B}}(B^0 \to
D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$ is measured
using a data sample of proton-proton collisions collected with the LHCb
detector at center-of-mass energies of 7 and 8 Tev, corresponding to an
integrated luminosity of 3$~$fb$^{-1}$. For the first time ${\cal{R}}(D^{*-})$
is determined using the $\tau$ lepton decays with three charged pions in the
final state. The $B^0 \to D^{*-} \tau^+\nu_{\tau}$ yield is normalized to that
of the $B^0\to D^{*-} \pi^+\pi^-\pi^+$ mode, providing a measurement of
${\cal{B}}(B^0\to D^{*-}\tau^+\nu_{\tau})/{\cal{B}}(B^0\to
D^{*-}\pi^+\pi^-\pi^+) = 1.97 \pm 0.13 \pm 0.18$, where the first uncertainty
is statistical and the second systematic. The value of ${\cal{B}}(B^0 \to
D^{*-} \tau^+ \nu_{\tau}) = (1.42 \pm 0.094 \pm 0.129 \pm 0.054)\% $ is
obtained, where the third uncertainty is due to the limited knowledge of the
branching fraction of the normalization mode. Using the well-measured branching
fraction of the $B^0 \to D^{*-} \mu^+\nu_{\mu}$ decay, a value of
${\cal{R}}(D^{*-}) = 0.291 \pm 0.019 \pm 0.026 \pm 0.013$ is established, where
the third uncertainty is due to the limited knowledge of the branching
fractions of the normalization and $B^0\to D^{*-}\mu^+\nu_{\mu}$ modes. This
measurement is in agreement with the Standard Model prediction and with
previous results.

Measurements of the cross-section for producing \bquark quarks in the
reaction $pp\to b\bar{b} X$ are reported in 7 and 13 TeV collisions at the LHC
as a function of the pseudorapidity $\eta$ in the range $2<\eta<5$ covered by
the acceptance of the LHCb experiment. The measurements are done using
semileptonic decays of $b$-flavored hadrons decaying into a ground-state
charmed hadron in association with a muon. The cross-sections in the covered
$\eta$ range are $72.0\pm 0.3\pm6.8~\mu$b and $144\pm 1\pm 21~\mu$b for 7 and
13 TeV. The ratio is $2.00\pm0.02\pm0.26$, where the quoted uncertainties are
statistical and systematic, respectively. The agreement with theoretical
expectation is good at 7 TeV, but differs somewhat at 13 TeV. The measured
ratio of cross-sections is larger at lower $\eta$ than the model prediction.

A search for $C\!P$ violation in the decay $\Lambda^0_b \to p K^- \mu^+
\mu^-$ is presented. This decay is mediated by flavour-changing neutral-current
transitions in the Standard Model and is potentially sensitive to new sources
of $C\!P$ violation. The study is based on a data sample of proton-proton
collisions recorded with the LHCb experiment, corresponding to an integrated
luminosity of $3$ $\mathrm{fb}^{-1}$. The $\Lambda^0_b \to p K^- \mu^+ \mu^-$
decay is observed for the first time, and two observables that are sensitive to
different manifestations of $C\!P$ violation are measured,
$\Delta\mathcal{A}_{C\!P} \equiv \mathcal{A}_{C\!P}(\Lambda^0_b \to p K^- \mu^+
\mu^-)-\mathcal{A}_{C\!P}(\Lambda^0_b\to pK^- J/\psi)$ and
$a_{C\!P}^{\widehat{T}-odd}$, where the latter is based on asymmetries in the
angle between the $\mu^+\mu^-$ and $p K^-$ decay planes. These are measured to
be $\Delta\mathcal{A}_{C\!P} = (-3.5 \pm 5.0(stat) \pm 0.2(syst))\times
10^{-2}$, $a_{C\!P}^{\widehat{T}-odd} = (1.2 \pm 5.0(stat) \pm 0.7(syst))\times
10^{-2}$, and no evidence for $C\!P$ violation is found.

Measurements of $CP$ observables in $B^{\pm} \rightarrow D K^{*\pm}$ decays
are presented, where $D$ denotes a superposition of $D^0$ and $\overline{D^0}$
meson states. Decays of the $D$ meson to $K^{-}\pi^{+}$, $K^{-}K^{+}$,
$\pi^{-}\pi^{+}$, $K^{-}\pi^{+}\pi^{-}\pi^{+}$ and
$\pi^{-}\pi^{+}\pi^{-}\pi^{+}$ are used and the $K^{*\pm}$ meson is
reconstructed in the $K^{0}_{\mathrm{S}}\pi^{\pm}$ final state. This analysis
uses a data sample of $pp$ collisions collected with the LHCb experiment,
corresponding to integrated luminosities of 1 $\mathrm{fb}^{-1}$, 2
$\mathrm{fb}^{-1}$ and 1.8 $\mathrm{fb}^{-1}$ at centre-of-mass energies
$\sqrt{s} = $ 7 TeV, 8 TeV and 13 TeV, respectively. The sensitivity of the
results to the CKM angle $\gamma$ is discussed.

A search for the lepton-flavour violating decays $B^0_s \rightarrow e^\pm
\mu^\mp$ and $B^0 \rightarrow e^\pm \mu^\mp$ is performed based on a sample of
proton-proton collision data corresponding to an integrated luminosity of 3
fb$^{-1}$, collected with the LHCb experiment at centre-of-mass energies of 7
and 8 TeV. The observed yields are consistent with the background-only
hypothesis. Upper limits on the branching fractions are determined to be
$\mathcal{B}(B^0_s \rightarrow e^\pm \mu^\mp) < 5.4\,(6.3) \times 10^{-9}$ and
$\mathcal{B}(B^0 \rightarrow e^\pm \mu^\mp) < 1.0\,(1.3) \times 10^{-9}$ at
$90\%\,(95\%)$ confidence level, which are the strongest limits on these decays
to date.

A measurement is reported of the ratio of branching fractions
$\mathcal{R}(J/\psi)=\mathcal{B}(B_c^+\,\to\,J/\psi\tau^+\nu_\tau)/\mathcal{B}(B_c^+\,\to\,J/\psi
\mu^+\nu_\mu)$, where the $\tau^+$ lepton is identified in the decay mode
$\tau^+\,\to\,\mu^+\nu_\mu\overline{\nu}_\tau$. This analysis uses a sample of
proton-proton collision data corresponding to 3.0$\mathrm{\,fb}^{-1}$ of
integrated luminosity recorded with the LHCb experiment at center-of-mass
energies $7\,\mathrm{TeV}$ and $8\,\mathrm{TeV}$. A signal is found for the
decay $B_c^+\,\to\,J/\psi \tau^+\nu_\tau$ at a significance of 3 standard
deviations, corrected for systematic uncertainty, and the ratio of the
branching fractions is measured to be $\mathcal{R}(J/\psi) = 0.71 \pm 0.17
\mathrm{\,(stat)} \pm 0.18\mathrm{\,(syst)}$. This result lies within 2
standard deviations above the range of existing predictions in the Standard
Model.

A measurement of the shape of the differential decay rate and the associated
Isgur-Wise function for the decay
$\Lambda_b^0\to\Lambda_c^+\mu^-\overline{\nu}$ is reported, using data
corresponding to $3 fb^{-1}$ collected with the LHCb detector in proton-proton
collisions. The $\Lambda_c^+\mu^-\overline{\nu}$(+ anything) final states are
reconstructed through the detection of a muon and a $\Lambda_c^+$ baryon
decaying into $pK^-\pi^+$, and the decays
$\Lambda_b^0\to\Lambda_c^+\pi^+\pi^-\mu^-\overline{\nu}$ are used to determine
contributions from $\Lambda_b^0\to \Lambda_c^{\star+}\mu ^-\bar{\nu}$ decays.
The measured dependence of the differential decay rate upon the squared
four-momentum transfer between the heavy baryons, $q^2$, is compared with
expectations from heavy-quark effective theory and from unquenched lattice QCD
predictions.

A search for charmless four-body decays of $\Lambda_{b}^{0}$ and
$\Xi_{b}^{0}$ baryons with a proton and three charged mesons (either kaons or
pions) in the final state is performed. The data sample used was recorded in
2011 and 2012 with the LHCb experiment and corresponds to an integrated
luminosity of 3 fb$^{-1}$. Six decay modes are observed, among which
$\Lambda_{b}^{0} \to pK^{-}\pi^{+}\pi^{-}$, $\Lambda_{b}^{0} \to
pK^{-}K^{+}K^{-}$, $\Xi_{b}^{0} \to pK^{-}\pi^{+}\pi^{-}$ and $\Xi_{b}^{0} \to
pK^{-} \pi^{+}K^{-}$ are established for the first time. Their branching
fractions (including the ratio of hadronisation fractions in the case of the
$\Xi_{b}^{0}$ baryon) are determined relative to the $\Lambda_{b}^{0} \to
\Lambda_{c}^{+}\pi^{-}$ decay.

Searches are performed for both prompt-like and long-lived dark photons,
$A^{\prime}$, produced in proton-proton collisions at a center-of-mass energy
of 13 TeV, using $A^{\prime}\to\mu^+\mu^-$ decays and a data sample
corresponding to an integrated luminosity of 1.6 fb$^{-1}$ collected with the
LHCb detector. The prompt-like $A^{\prime}$ search covers the mass range from
near the dimuon threshold up to 70 GeV, while the long-lived $A^{\prime}$
search is restricted to the low-mass region $214<m(A^{\prime})<350$ MeV. No
evidence for a signal is found, and 90% confidence level exclusion limits are
placed on the $\gamma$-$A^{\prime}$ kinetic-mixing strength. The constraints
placed on prompt-like dark photons are the most stringent to date for the mass
range $10.6 < m(A^{\prime}) < 70$ GeV, and are comparable to the best existing
limits for $m(A^{\prime}) < 0.5$ GeV. The search for long-lived dark photons is
the first to achieve sensitivity using a displaced-vertex signature.

The decay $Z \rightarrow b \bar{b}$ is reconstructed in $pp$ collision data,
corresponding to 2 fb$^{-1}$ of integrated luminosity, collected by the LHCb
experiment at a centre-of-mass energy of $\sqrt{s}=8$ TeV. The product of the
$Z$ production cross-section and the $Z \rightarrow b \bar{b}$ branching
fraction is measured for candidates in the fiducial region defined by two
particle-level $b$-quark jets with pseudorapidities in the range $2.2 < \eta <
4.2$, with transverse momenta $p_{T}>20$ GeV and dijet invariant mass in the
range $45 < m_{jj} < 165$ GeV. From a signal yield of $5462 \pm 763$ $Z
\rightarrow b \bar{b}$ events, where the uncertainty is statistical, a
production cross-section times branching fraction of $332 \pm 46 \pm 59$ pb is
obtained, where the first uncertainty is statistical and the second systematic.
The measured significance of the signal yield is 6.0 standard deviations. This
measurement represents the first observation of the $Z \rightarrow b \bar{b}$
production in the forward region of $pp$ collisions.

A search for $B^{+} \to D_s^{+}K^{+}K^{-}$ decays is performed using $pp$
collision data corresponding to an integrated luminosity of 4.8 fb$^{-1}$,
collected at centre-of-mass energies of 7, 8 and 13$\,$TeV with the LHCb
experiment. A significant signal is observed for the first time and the
branching fraction is determined to be \begin{equation*} \mathcal{B}(B^{+} \to
D_s^{+}K^{+}K^{-} ) = (7.1 \pm 0.5 \pm 0.6 \pm 0.7) \times 10^{-6},
\end{equation*} where the first uncertainty is statistical, the second
systematic and the third due to the uncertainty on the branching fraction of
the normalisation mode $B^{+} \to D_s^{+} \overline{\kern -0.2em D}^{0}$. A
search is also performed for the pure annihilation decay $B^{+} \to
D_s^{+}\phi$. No significant signal is observed and a limit of
\begin{equation*} \mathcal{B}(B^{+} \to D_s^{+}\phi) < 4.9 \times 10^{-7}~(4.2
\times 10^{-7}) \end{equation*} is set on the branching fraction at 95$\%$
(90$\%$) confidence level.

A measurement is presented of decay-time-dependent $CP$ violation in the
decays $B^0\rightarrow J/\psi K^0_\mathrm{S}$ and $B^0\rightarrow\psi(2S)
K^0_\mathrm{S}$, where the $J/\psi$ is reconstructed from two electrons and the
$\psi(2S)$ from two muons. The analysis uses a sample of $pp$ collision data
recorded with the LHCb experiment at centre-of-mass energies of 7 and 8 TeV,
corresponding to an integrated luminosity of 3 $\mathrm{fb}^{-1}$. The
$CP$-violation observables are measured to be \begin{equation*} \begin{aligned}
C\left(B^0\rightarrow J/\psi
K^0_\mathrm{S}\right)&=\phantom{+}\,0.12\,\pm\,0.07\pm\,0.02\,,
S\left(B^0\rightarrow J/\psi
K^0_\mathrm{S}\right)&=\phantom{+}\,0.83\,\pm\,0.08\pm\,0.01\,,
C\left(B^0\rightarrow\psi(2S)
K^0_\mathrm{S}\right)&=-\,0.05\,\pm\,0.10\pm\,0.01\,,
S\left(B^0\rightarrow\psi(2S)
K^0_\mathrm{S}\right)&=\phantom{+}\,0.84\,\pm\,0.10\pm\,0.01\,, \end{aligned}
\end{equation*} where $C$ describes $CP$ violation in the direct decay, and $S$
describes $CP$ violation in the interference between the amplitudes for the
direct decay and for the decay after $B^0$-$\overline{B}^0$ oscillation. The
first uncertainties are statistical and the second are systematic. The two sets
of results are compatible with the previous LHCb measurement using
$B^0\rightarrow J/\psi K^0_\mathrm{S}$ decays, where the $J/\psi$ meson was
reconstructed from two muons. The averages of all three sets of LHCb results
are \begin{equation*} \begin{aligned}
C\left(B^0\rightarrow[c\bar{c}]K^0_\mathrm{S}\right)&=-0.017 \pm 0.029\,,
S\left(B^0\rightarrow[c\bar{c}]K^0_\mathrm{S}\right)&=\phantom{+}0.760 \pm
0.034\,, \end{aligned} \end{equation*} under the assumption that higher-order
contributions to the decay amplitudes are negligible. The uncertainties include
statistical and systematic contributions.

The time-integrated Dalitz plot of the three-body hadronic charmless decay
${{\overline{B}}^0 \to K_{\mathrm{\scriptscriptstyle S}}^0 \pi^+ \pi^-}$ is
studied using a $pp$ collision data sample recorded with the LHCb detector,
corresponding to an integrated luminosity of $3.0\;\mathrm{fb}^{-1}$. The decay
amplitude is described with an isobar model. Relative contributions of the
isobar amplitudes to the ${\overline{B}^0 \to K_{\mathrm{\scriptscriptstyle
S}}^0 \pi^+ \pi^-}$ decay branching fraction and CP asymmetries of the
flavour-specific amplitudes are measured. The CP asymmetry between the
conjugate ${\overline{B}^0 \to K^{*}(892)^{-}\pi^+}$ and ${\overline{B}^0 \to
K^{*}(892)^{+}\pi^-}$ decay rates is determined to be $-0.308 \pm 0.062$.

The polarization of the $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)
$mesons, produced in $pp$ collisions at centre-of-mass energies $\sqrt{s}$=7
and 8TeV, is measured using data samples collected by the LHCb experiment,
corresponding to integrated luminosities of 1 and 2fb$^{-1}$, respectively. The
measurements are performed in three polarization frames, using
$\Upsilon\to\mu^+\mu^-$ decays in the kinematic region of the transverse
momentum $p_{T}(\Upsilon)<30GeV/c$, and rapidity $2.2<y(\Upsilon)<4.5$. No
large polarization is observed.

A search for the decay $K^0_{\scriptscriptstyle S}\to\mu^+\mu^-$ is
performed, based on a data sample of proton-proton collisions corresponding to
an integrated luminosity of 3 fb$^{-1}$, collected by the LHCb experiment at
centre-of-mass energies of 7 and 8 TeV. The observed yield is consistent with
the background-only hypothesis, yielding a limit on the branching fraction of
${\cal B}(K^0_{\scriptscriptstyle S}\to\mu^+\mu^-) < 0.8~(1.0) \times 10^{-9}$
at $90\%~(95\%)$ confidence level. This result improves the previous upper
limit on the branching fraction by an order of magnitude.

The production of $B^{\pm}$ mesons is studied in $pp$ collisions at
centre-of-mass energies of 7 and 13 TeV, using $B^{\pm}\rightarrow J/\psi
K^{\pm}$ decays and data samples corresponding to 1.0 fb$^{-1}$ and 0.3
fb$^{-1}$, respectively. The production cross-sections summed over both charges
and integrated over the transverse momentum range $0<p_{\text{T}}< 40$ GeV/$c$
and the rapidity range $2.0<y<4.5$ are measured to be
$\sigma(pp \rightarrow B^{\pm} X, \sqrt{s} = \text{7 TeV}) = 43.0 \pm 0.2 \pm
2.5 \pm 1.7\mu b,$
$\sigma(pp \rightarrow B^{\pm} X, \sqrt{s} = \text{13 TeV}) = 86.6 \pm 0.5
\pm 5.4 \pm 3.4\mu b,$
where the first uncertainties are statistical, the second are systematic, and
the third are due to the limited knowledge of the $B^{\pm}\rightarrow J/\psi
K^{\pm}$ branching fraction. The ratio of the cross-section at 13 TeV to that
at 7 TeV is determined to be $2.02\pm0.02\text{(stat)}\pm0.12\text{(syst)}$.
Differential cross-sections are also reported as functions of $p_{\text{T}}$
and $y$. All results are in agreement with theoretical calculations based on
the state-of-art fixed next-to-leading order quantum chromodynamics.

The $B^+ \to D^{*-}K^+\pi^+$ decay potentially provides an excellent way to
investigate charm meson spectroscopy. The decay is searched for in a sample of
proton-proton collision data collected with the LHCb detector at centre-of-mass
energies of 7 and 8 TeV, corresponding to an integrated luminosity of $3~{\rm
fb}^{-1}$. A clear signal is observed, and the ratio of its branching fraction
to that of the $B^+ \to D^{*-}\pi^+\pi^+$ normalisation channel is measured to
be \begin{equation*}
\frac{\mathcal{B}(B^+ \to D^{*-}K^+\pi^+)}{\mathcal{B}(B^+ \to
D^{*-}\pi^+\pi^+)} = \left( 6.39 \pm 0.27 \pm 0.48 \right) \times 10^{-2} \, ,
\end{equation*} where the first uncertainty is statistical and the second is
systematic. This is the first observation of the $B^+ \to D^{*-}K^+\pi^+$
decay.

Using decays to $\phi$-meson pairs, the inclusive production of charmonium
states in $b$-hadron decays is studied with $pp$ collision data corresponding
to an integrated luminosity of $3.0fb^{-1}$, collected by the LHCb experiment
at centre-of-mass energies of 7 and 8 TeV. Denoting by $B_C\equiv B(b\to
CX)\times B(C\to\phi\phi)$ the inclusive branching fraction of a $b$ hadron to
a charmonium state $C$ that decays into a pair of $\phi$ mesons, ratios
$R^{C1}_{C2}\equiv B_{C1}/B_{C2}$ are determined as
$R^{\chi_{c0}}_{\eta_c(1S)}=0.147\pm0.023\pm0.011$, $R^{\chi_{c1}}_{\eta_c
(1S)}=0.073\pm0.016\pm0.006$, $R^{\chi_{c2}}_{\eta_c
(1S)}=0.081\pm0.013\pm0.005$, $R^{\chi_{c1}}_{\chi_{c0}}=0.50\pm0.11\pm0.01$,
$R^{\chi_{c2}}_{\chi_{c0}}=0.56\pm0.10\pm0.01$ and $R^{\eta_c
(2S)}_{\eta_c(1S)}=0.040\pm0.011\pm0.004$. Here and below the first
uncertainties are statistical and the second systematic. Upper limits at $90\%$
confidence level for the inclusive production of $X(3872)$, $X(3915)$ and
$\chi_{c2}(2P)$ states are obtained as $R^{X(3872)}_{\chi_{c1}}<0.34$,
$R^{X(3915)}_{\chi_{c0}}<0.12$ and $R^{\chi_{c2}(2P)}_{\chi_{c2}}<0.16$.
Differential cross-sections as a function of transverse momentum are measured
for the $\eta_c(1S)$ and $\chi_c$ states. The branching fraction of the decay
$B_s^0\rightarrow\phi\phi\phi$ is measured for the first time,
$B(B_s^0\to\phi\phi\phi)=(2.15\pm0.54\pm0.28\pm0.21_{B})\times 10^{-6}$. Here
the third uncertainty is due to the branching fraction of the decay
$B_s^0\to\phi\phi$, which is used for normalization. No evidence for
intermediate resonances is seen. A preferentially transverse $\phi$
polarization is observed. The measurements allow the determination of the ratio
of the branching fractions for the $\eta_c(1S)$ decays to $\phi\phi$ and
$p\bar{p}$ as $B(\eta_c(1S)\to\phi\phi)/B(\eta_c(1S)\to
p\bar{p})=1.79\pm0.14\pm0.32$.